Evaluate ∫x−$$131+x1/31/4dx$$

Correct option is 4None of the above

Questions

Evaluate $\int x^{\frac{- 1}{3}} {(1 + x^{1 / 3})}^{1 / 4} dx$

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−4151+x1/35/44+9x1/2+C

1151+x1/35/44+9x1/3+C

2151+x1/31/44+9x1/3+C

None of the above

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detailed solution

Correct option is D

Here, m=−13,n=13,p=14,m+1n=2Which is an integer.So, 1+x1/3=t4⇒ dx3x2/3=4t3dtI=12∫t4−1t4dtI=12t8−t4⋅dt=12t99−t55+C ∵C=12C1=4t5t43−35+C=4151+x1/35/4⋅5x1/3−4

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Evaluate ∫x−131+x1/31/4dx

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Evaluate $\int x^{\frac{- 1}{3}} {(1 + x^{1 / 3})}^{1 / 4} dx$